When Kernel Ridge Regression Meets the Holder-Zygmund Class: Minimax Optimality and Failure of Properness

arXiv:2607.26065v1 Announce Type: cross Abstract: We study kernel ridge regression for nonparametric regression over the Holder-Zygmund class. Using an RKHS equivalent to a Sobolev space of smoothness s+d/2, we prove that misspecified KRR attains the minimax L2 rate n^{-2s/(2s+d)}. We also show that properness fails in the Holder-Zygmund norm: even for the zero regression function with Gaussian noise, the expected squared Holder-Zygmund norm of the KRR noise component grows as log n.

Source: arXiv cs.LG | 2026-07-30